Regents Exam Questions
G.G.37: Interior and Exterior Angles of Polygons
Name: ________________________
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G.G.37: Interior and Exterior Angles of Polygons: Investigate, justify, and apply theorems about
each interior and exterior angle measure of regular polygons
1 What is the measure of each interior angle in a
regular octagon?
1) 108º
2) 135º
3) 144º
4) 1080º
6 In the diagram below of regular pentagon ABCDE,
EB is drawn.
2 What is the measure of an interior angle of a
regular octagon?
1) 45º
2) 60º
3) 120º
4) 135º
What is the measure of ∠AEB?
1) 36º
2) 54º
3) 72º
4) 108º
3 What is the measure of each interior angle of a
regular hexagon?
1) 60°
2) 120°
3) 135°
4) 270°
7 What is the measure, in degrees, of each exterior
angle of a regular hexagon?
1) 45
2) 60
3) 120
4) 135
4 Determine, in degrees, the measure of each interior
angle of a regular octagon.
5 Determine and state the measure, in degrees, of an
interior angle of a regular decagon.
8 A stop sign in the shape of a regular octagon is
resting on a brick wall, as shown in the
accompanying diagram.
What is the measure of angle x?
1) 45°
2) 60°
3) 120°
4) 135°
1
Regents Exam Questions
G.G.37: Interior and Exterior Angles of Polygons
Name: ________________________
www.jmap.org
13 The measure of an interior angle of a regular
polygon is 120°. How many sides does the polygon
have?
1) 5
2) 6
3) 3
4) 4
9 One piece of the birdhouse that Natalie is building
is shaped like a regular pentagon, as shown in the
accompanying diagram.
14 Melissa is walking around the outside of a building
that is in the shape of a regular polygon. She
determines that the measure of one exterior angle
of the building is 60°. How many sides does the
building have?
1) 6
2) 9
3) 3
4) 12
If side AE is extended to point F, what is the
measure of exterior angle DEF?
1) 36°
2) 72°
3) 108°
4) 144°
15 A regular polygon has an exterior angle that
measures 45°. How many sides does the polygon
have?
1) 10
2) 8
3) 6
4) 4
10 What is the difference between the sum of the
measures of the interior angles of a regular
pentagon and the sum of the measures of the
exterior angles of a regular pentagon?
1) 36
2) 72
3) 108
4) 180
16 A regular polygon with an exterior angle of 40° is a
1) pentagon
2) hexagon
3) nonagon
4) decagon
11 Find, in degrees, the measures of both an interior
angle and an exterior angle of a regular pentagon.
17 What is the measure of the largest exterior angle
that any regular polygon can have?
1) 60º
2) 90º
3) 120º
4) 360º
12 The sum of the interior angles of a regular polygon
is 720°. How many sides does the polygon have?
1) 8
2) 6
3) 5
4) 4
18 The sum of the interior angles of a regular polygon
is 540°. Determine and state the number of degrees
in one interior angle of the polygon.
2
ID: A
G.G.37: Interior and Exterior Angles of Polygons: Investigate, justify, and apply theorems about
each interior and exterior angle measure of regular polygons
Answer Section
1 ANS: 2
1080
= 135.
8
(n − 2)180 = (8 − 2)180 = 1080.
REF: 081521ge
2 ANS: 4
1080
= 135.
8
(n − 2)180 = (8 − 2)180 = 1080.
REF: fall0827ge
3 ANS: 2
(n − 2)180 = (6 − 2)180 = 720.
720
= 120.
6
REF: 081125ge
4 ANS:
1080
= 135.
8
(n − 2)180 = (8 − 2)180 = 1080.
REF: 061330ge
5 ANS:
(n − 2)180 (10 − 2)180
=
= 144
10
n
REF: 011531ge
6 ANS: 1
(n − 2)180 (5 − 2)180
180 − 108
∠A =
=
= 108 ∠AEB =
= 36
2
n
5
REF: 081022ge
7 ANS: 2
(n − 2)180 = (6 − 2)180 = 720.
REF: 060213a
8 ANS: 1
(n − 2)180 = (8 − 2)180 = 1080.
720
= 120. 180 − 120 = 60.
6
1080
= 135. 180 − 45 = 135.
8
REF: 080507a
1
ID: A
9 ANS: 2
(n − 2)180 = (5 − 2)180 = 540.
540
= 108. 180 − 108 = 72.
5
REF: 060718a
10 ANS: 4
 (n − 2)180 
 = 180n − 360 − 180n + 180n − 360 = 180n − 720.
(n − 2)180 − n 


n


180(5) − 720 = 180
REF: 081322ge
11 ANS:
(5 − 2)180 = 540.
540
= 108 interior. 180 − 108 = 72 exterior
5
REF: 011131ge
12 ANS: 2
180(n − 2) = 720
n−2= 4
n=6
REF: 061521ge
13 ANS: 2
(n − 2)180
= 120 .
n
180n − 360 = 120n
60n = 360
n=6
REF: 011326ge
14 ANS: 1
Find an interior angle. 180 − x = 60 . Find n.
x = 120
(n − 2)180
= 120 .
n
180n − 360 = 120n
60n = 360
n=6
REF: 060423a
2
ID: A
15 ANS: 2
(n − 2)180
180 −
= 45
n
180n − 180n + 360 = 45n
360 = 45n
n=8
REF: 061413ge
16 ANS: 3
(n − 2)180
180 −
= 40
n
180n − 180n + 360 = 40n
360 = 40n
n=9
REF: 061519ge
17 ANS: 3
The regular polygon with the smallest interior angle is an equilateral triangle, with 60º. 180° − 60° =120°
REF: 011417ge
18 ANS:
(n − 2)180 = 540.
n−2= 3
540
= 108
5
n=5
REF: 081434ge
3